question 25 of 40\na student was given two data sets, set a and set b. which of the following statements is…

question 25 of 40\na student was given two data sets, set a and set b. which of the following statements is true?\nset a\n|x|0|1|2|3|4|\n|y|10|20|30|40|50|\nset b\n|x|0|1|2|3|4|\n|y|2|10|50|250|1250|\na. set a is a linear function and the values increase at a slower rate than set b.\nb. set a is a linear function and the values increase at a faster rate than set b.\nc. set b is an exponential function and the values increase at the same rate as set a.\nd. set b is an exponential function and the values increase at a slower rate than set a.

question 25 of 40\na student was given two data sets, set a and set b. which of the following statements is true?\nset a\n|x|0|1|2|3|4|\n|y|10|20|30|40|50|\nset b\n|x|0|1|2|3|4|\n|y|2|10|50|250|1250|\na. set a is a linear function and the values increase at a slower rate than set b.\nb. set a is a linear function and the values increase at a faster rate than set b.\nc. set b is an exponential function and the values increase at the same rate as set a.\nd. set b is an exponential function and the values increase at a slower rate than set a.

Answer

Explanation:

Step1: Determine the function type of Set A

For Set A, when (x) increases by 1 each time ((x = 0,1,2,3,4)), (y) increases by 10 each time ((y=10,20,30,40,50)). The rate of change (\frac{\Delta y}{\Delta x}=\frac{20 - 10}{1-0}=10). The equation of the line is (y=10x + 10) (using the slope - intercept form (y=mx + b), where (m = 10) and (b = 10) when (x = 0,y=10)), so Set A is a linear function.

Step2: Determine the function type of Set B

For Set B, when (x = 0,y = 2); when (x=1,y = 10) (a factor of 5 increase since (\frac{10}{2}=5)); when (x = 2,y=50) (a factor of 5 increase from (y = 10) since (\frac{50}{10}=5)); when (x=3,y = 250) (a factor of 5 increase from (y = 50) since (\frac{250}{50}=5)); when (x = 4,y=1250) (a factor of 5 increase from (y = 250) since (\frac{1250}{250}=5)). The equation of the function is (y=2\times5^{x}), so Set B is an exponential function.

Step3: Compare the rates of increase

The linear function in Set A has a constant rate of change of 10. The exponential function in Set B has a multiplicative rate of change of 5, and as (x) gets larger, the values of the exponential function in Set B will grow much faster than the linear function in Set A.

Answer:

A. Set A is a linear function and the values increase at a slower rate than Set B.